16-1

1 16-1 16 Residence TimeDistributions ofChemical Reactors Nothing in life is to be feared. It is only to be understood. Marie Curie General Considerations The reactors treated in the book thus far the perfectly mixed batch, theplug-flow tubular, the packed bed, and the perfectly mixed continuous tankreactors have been modeled as ideal reactors. Unfortunately, in the real worldOverview. In this chapter we learn about nonideal reactors; that is, reactorsthat do not follow the models we have developed for ideal CSTRs, PFRs, andPBRs. After studying this chapter the reader will be able to describe: General Considerations. How the residence time distribution (RTD)can be used (Section ). Measurement of the RTD. How to calculate the concentration curve( , the C-curve) and residence time distribution curve, ( , theE-curve (Section )).

2 Characteristics of the RTD. How to calculate and use the cumula-tive RTD function, F(t), the mean residence time, tm, and the vari-ance 2 (Section ). The RTD in ideal reactors. How to evaluate E(t), F(t), tm, and 2 forideal PFRs, CSTRs, and laminar flow reactors (LFRs) so that wehave a reference point as to how much our real ( , nonideal) reac-tor deviates form an ideal reactor (Section ). How to diagnose problems with real reactors by comparing tm, E(t),and F(t) with ideal reactors. This comparison will help to diagnoseand troubleshoot by-passing and dead volume problems in realreactors (Section ). Page 1 Tuesday, March 14, 2017 6:24 PM 16-2 Residence Time Distributions of Chemical ReactorsChapter 16 we often observe behavior very different from that expected from the exem-plar; this behavior is true of students, engineers, college professors, and chem-ical reactors.

3 Just as we must learn to work with people who are not perfect, so the reactor analyst must learn to diagnose and handle chemical reactorswhose performance deviates from the ideal. Nonideal reactors and the princi-ples behind their analysis form the subject of this chapter and the next basic ideas that are used in the distribution of residence times to char-acterize and model nonideal reactions are really few in number. The two majoruses of the residence time distribution to characterize nonideal reactors are1. To diagnose problems of reactors in To predict conversion or effluent concentrations in existing/availablereactors when a new chemical reaction is used in the following two examples illustrate reactor problems one might f indin a chemical plant.

4 Example 1 A packed-bed reactor is shown in Figure 16-1. When a reactor ispacked with catalyst, the reacting fluid usually does not flow uniformlythrough the reactor. Rather, there may be sections in the packed bed that offerlittle resistance to flow (Path 1) and, as a result, a portion of the fluid may chan-nel through this pathway. Consequently, the molecules following this pathwaydo not spend much time in the reactor. On the other hand, if there is internalcirculation or a high resistance to flow, the molecules could spend a long timein the reactor (Path 2). Consequently, we see that there is a distribution of timesthat molecules spend in the reactor in contact with the catalyst.

5 Example 2 In many continuous-stirred tank reactors, the inlet and outletpipes are somewhat close together (Figure 16-2). In one operation, it wasdesired to scale up pilot plant results to a much larger system. It was realizedthat some short-circuiting occurred, so the tanks were modeled as perfectlymixed CSTRs with a bypass stream. In addition to short-circuiting, stagnantregions (dead zones) are often encountered. In these regions, there is little orno exchange of material with the well-mixed regions and, consequently, virtu-ally no reaction occurs there. Experiments were carried out to determine theamount of the material effectively bypassed and the volume of the dead zone.

6 See the AIChE webinar Dealing with Diff icult People : icult-people .We want to analyzeand characterizenonideal 16-1 Packed-bed 1 Path 2 Page 2 Tuesday, March 14, 2017 6:24 PM Section Considerations 16-3 A simple modif ication of an ideal reactor successfully modeled the essentialphysical characteristics of the system and the equations were readily concepts were used to describe nonideal reactors in these exam-ples: the distribution of residence times in the system (RTD), the quality of mixing , and the model used to describe the system . All three of these concepts are consideredwhen describing deviations from the mixing patterns assumed in ideal reac-tors. The three concepts can be regarded as characteristics of the mixing innonideal way to order our thinking on nonideal reactors is to consider mod-eling the flow patterns in our reactors as either ideal CSTRs or PFRs as a f irst approximation.

7 In real reactors, however, nonideal flow patterns exist, result-ing in ineffective contacting and lower conversions than in the case of idealreactors. We must have a method of accounting for this nonideality, and toachieve this goal we use the next-higher level of approximation, which involvesthe use of macromixing information (RTD) (Sections to ). The next leveluses microscale ( micromixing ) information (Chapter 17) to make predictionsabout the conversion in nonideal reactors. After completing the f irst four sec-tions, through , the reader can proceed directly to Chapter 17 to learnhow to calculate the conversion and product distributions exiting real closes the chapter by discussing how to use the RTD to diagnoseand troubleshoot reactors.

8 Here, we focus on two common problems: reactorswith bypassing and dead volumes. Once the dead volumes, V D , and bypassingvolumetric flow rates, b , are determined, the strategies in Chapter 18 to modelthe real reactor with ideal reactors can be used to predict conversion. Time Distribution (RTD) Function The idea of using the distribution of residence times in the analysis of chem-ical reactor performance was apparently f irst proposed in a pioneering paperby MacMullin and Weber. 1 However, the concept did not appear to be usedextensively until the early 1950s, when Prof. P. V. Danckwerts gave organiza-tional structure to the subject of RTD by def ining most of the distributionsof interest. 2 The ever-increasing amount of literature on this topic since then There are a number of mixing tutorials on the AIChE Webinar website and as anAIChE student member you have free access to all these webinars.

9 See . 1 R. B. MacMullin and M. Weber, Jr., Trans. Am. Inst. Chem. Eng. , 31, 409 (1935). 2 P. V. Danckwerts, Chem. Eng. Sci. , 2, 1 (1953).DeadzoneBypassingFigure want to findways of determin-ing the dead zonevolume and thefraction of thevolumetric flowrate bypassing three concepts RTD Mixing ModelChance Card:Do not pass go,proceed directly toChapter Page 3 Tuesday, March 14, 2017 6:24 PM 16-4 Residence Time Distributions of Chemical ReactorsChapter 16 has generally followed the nomenclature of Danckwerts, and this will bedone here as an ideal plug-flow reactor, all the atoms of material leaving the reactorhave been inside it for exactly the same amount of time. Similarly, in an idealbatch reactor, all the atoms of materials within the reactor have been inside theBR for an identical length of time.

10 The time the atoms have spent in the reactoris called the residence time of the atoms in the idealized plug-flow and batch reactors are the only two types of reac-tors in which all the atoms in the reactors have exactly the same residencetime. In all other reactor types, the various atoms in the feed spend differenttimes inside the reactor; that is, there is a distribution of residence times of thematerial within the reactor. For example, consider the CSTR; the feed intro-duced into a CSTR at any given time becomes completely mixed with thematerial already in the reactor. In other words, some of the atoms entering theCSTR leave it almost immediately because material is being continuously with-drawn from the reactor; other atoms remain in the reactor almost foreverbecause all the material recirculates within the reactor and is virtually neverremoved from the reactor at one time.